Question

A pendulum clock made up of metal gives correct time at 30 degree Celsius if room temperature rises to 40 degree Celsius then error in clock per 10 hour would be( Alpha= 10^-3/°C​

Answer 1

error would be 0.05 hrs per 10 hours.

it is given that,

initial temperature, Ti = 30°C

final temperature, Tf = 40°C

coefficient of linear expansion, α = 10-³/°C

as we know, time period, T = 2π√{L/g}......(1)

so time period after increasing temperature, ∆θ = T' = 2π√{L(1 + α(Tf - Ti)/g}

= 2π√{L/g}(1 + α/2(Tf - Ti))

= T{1 + α/2(Tf - Ti)}

or, ∆T/T = α/2(Tf - Ti)

⇒∆T/10 hours = 10^-3 × 1/2 (40 - 30)

⇒∆T = 10^-3 × 10 × 10/2 = 0.1/2 = 0.05 hours

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Answer 2

$\huge\bold\purple{Answer:-}$

it is given that,

initial temperature, Ti = 30°C

final temperature, Tf = 40°C

coefficient of linear expansion, α = 10-³/°C

as we know, time period, T = 2π√{L/g}......(1)

so time period after increasing temperature, ∆θ = T' = 2π√{L(1 + α(Tf - Ti)/g}

= 2π√{L/g}(1 + α/2(Tf - Ti))

= T{1 + α/2(Tf - Ti)}

or, ∆T/T = α/2(Tf - Ti)

⇒∆T/10 hours = 10^-3 × 1/2 (40 - 30)

⇒∆T = 10^-3 × 10 × 10/2 = 0.1/2 = 0.05 hours